A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Classifies Lie symmetry algebras for 2D quasilinear equations, linking symmetry to linearity.
Study finds index of symmetry for solvable 3D Lie groups with left-invariant metrics.
Reduces equations for contact mechanical systems on Lie groups by exploiting symmetries.
The paper analyzes Lie symmetries in a specific geometric context.
The paper analyzes symmetries of Vaidya-Bonner geodesics.
Researchers discover symmetries in Ricci flows and use them to find invariant solutions.
Paper studies symmetries in singular foliations using Lie -morphisms.
Study 2D viscoelastic equations using Lie group theory.
We study Lie algebras of generators of infinitesimal symmetries of almost-cosymplectic-contact structures of odd dimensional manifolds. The almost-cosymplectic-contact structure admits on the sheaf of pairs of 1-forms and functions the structure of a Lie algebra. We describe Lie subalgebras in this Lie algebra given by…
Lie symmetry group method is applied to study the Born-Infeld equation. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra symmetries is determined.
We describe the reduction procedure for a symplectic Lie algebroid by a Lie subalgebroid and a symmetry Lie group. Moreover, given an invariant Hamiltonian function we obtain the corresponding reduced Hamiltonian dynamics. Several examples illustrate the generality of the theory.
This work presents a geometrical formulation of the Clairin theory of conditional symmetries for higher-order systems of partial differential equations (PDEs). We devise methods for obtaining Lie algebras of conditional symmetries from known conditional symmetries, and unnecessary previous assumptions of the theory are…
Classifies flat projective structures with specific symmetries.
In this paper, a complete Lie symmetry analysis of the damped wave equation with time-dependent coefficients is investigated. Then the invariant solutions and the exact solutions generated from the symmetries are presented. Moreover, a Lie algebraic classifications and the optimal system are discussed. Finally, using C…
Investigates geometric mean reversion process using Lie symmetry method.
Study of symmetries in 3D Lie groups, determining index and moduli space properties.
The paper realizes Lie superalgebras G(3) and F(4) as symmetries of supergeometries.
We show that a certain symmetry exists in the stable irreducible decomposition of the Lie algebra consisting of symplectic derivations of the free Lie algebra generated by the first homology group of compact oriented surfaces.
The theory of Lie remarkable equations, i.e. differential equations characterized by their Lie point symmetries, is reviewed and applied to ordinary differential equations. In particular, we consider some relevant Lie algebras of vector fields on and characterize Lie remarkable equations admitted by the …
Machine learning explores symmetries in field theory and algebra.
This paper classifies symmetries of biharmonic heat equations on surfaces of revolution.
We determine the index of symmetry of 3-dimensional unimodular Lie groups with a left-invariant metric. In particular, we prove that every 3-dimensional unimodular Lie group admits a left-invariant metric with positive index of symmetry. We also study the geometry of the quotients by the so-called foliation of symmetry…
Describes reconstructing Poisson structures from Lie group actions.
The paper discusses reducing Hamiltonian systems by scaling and standard symmetries, leading to Kirillov Hamiltonian systems.
We discuss various compatibility criteria for overdetermined systems of PDEs generalizing the approach to formal integrability via brackets of differential operators. Then we give sufficient conditions that guarantee that a PDE possessing a Lie algebra of symmetries has invariant solutions with respect to this Lie alge…
Unified framework for enforcing, discovering, and promoting symmetry in machine learning.
Reduces multisymplectic Lie systems through symmetry analysis.
Geometric framework for dynamic feedback linearization of control systems with symmetry.
We study the interplay between the differential Galois group and the Lie algebra of infinitesimal symmetries of systems of linear differential equations. We show that some symmetries can be seen as solutions of a hierarchy of linear differential systems. We show that the existence of rational symmetries constrains the …
We perform a classification of the Lie point symmetries for the Black--Scholes--Merton Model for European options with stochastic volatility, , in which the last is defined by a stochastic differential equation with an Orstein--Uhlenbeck term. In this model, the value of the option is given by a linear (1 + 2) evolu…
In this paper we investigate the relations between semispray, nonlinear connection, dynamical covariant derivative and Jacobi endomorphism on Lie algebroids. Using these geometric structures, we study the symmetries of second order differential equations in the general framework of Lie algebroids.
The study explores maximal symmetry in Ricci solitons on Lie groups.
This research introduces Lie brackets on spaces of biderivations in Lie algebras.
Classifies Lie algebras and related spacetimes for a specific type of symmetry.
New internal symmetry found for Lie pair algebra.
In this article we consider nonholonomic deformations of disk solutions in general relativity to generic off-diagonal metrics defining knew classes of exact solutions in 4D and 5D gravity. These solutions possess Lie algebroid symmetries and local anisotropy and define certain generalizations of manifolds with Killing …
New knot invariants discovered using mirror symmetry.
This research extends Lie algebra actions to singular foliations.
Study of Morita equivalences in Lie groupoids and their symmetries.
We use Lie symmetry methods to price certain types of barrier options. Usually Lie symmetry methods cannot be used to solve the Black-Scholes equation for options because the function defining the maturity condition for an option is not smooth. However, for barrier options, this restriction can be accommodated and a sy…
In this paper, Lie symmetry group method is applied to find the lie point symmetries group of a PDE system that is determined general form of four-dimensional Einstein Walker manifold. Also we will construct the optimal system of one-dimensional Lie subalgebras and investigate some of its group invariant solutions.
The paper studies symmetry reduction and optimal control on Riemannian manifolds.
We generalize the symmetry superalgebras of isometries and geometric Killing spinors on a manifold to include all the hidden symmetries of the manifold generated by Killing spinors in all dimensions. We show that bilinears of geometric Killing spinors produce special Killing-Yano and special conformal Killing-Yano form…
Study of symmetry distributions in Lorentzian naturally reductive nilmanifolds.
In this paper, a complete analysis of symmetries and conservation laws for the charged squashed Kaluza--Klein black hole spacetime in a Riemannian space is discussed. First, a comprehensive group analysis of the underlying space-time metric using Lie point symmetries are presented and then it the -dimensional optima…
In this paper we parametrize the symmetry group of the n-dimensional Berwald-Moor metric. Some properties of this Lie group are studied, and its corresponding Lie algebra is computed.
We show that the distribution of symmetry of a naturally reductive nilpotent Lie group coincides with the invariant distribution induced by the set of fixed vectors of the isotropy. This extends a known result on compact naturally reductive spaces. We also address the study of the quotient by the foliation of symmetry.
Recently, it was shown that Einstein solvmanifolds have maximal symmetry in the sense that their isometry groups contain the isometry groups of any other left-invariant metric on the given Lie group. Such a solvable Lie group is necessarily non-unimodular. In this work we consider unimodular solvable Lie groups and pro…